In a known machine tool described in German Offenlegungsschrift No. 3,411,647, the spindle head can pivot 180 degrees relative to the carrier. The tool spindle is thereby brought from a vertical into a horizontal position. During machining, coolant is often required in the working zone of the tools. For machining deep bores or in machining work carried out inside housing, it is highly advantageous if the coolant is conveyed through the interior of the tool into the vicinity of the tool tip. The coolant is thus supplied to the tool through the working spindle (as discussed in German Utility Model No. 8,430,433), this being the so-called internal coolant supply. The hitherto known designs with internal coolant supply have relatively large overall length and are therefore unsuitable for machine tools.